Educ. Reso. for Part. Techn. 012Q-Rhodes

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Copyright © 2001 Martin Rhodes, Licensed to ERPT

Fluidization of Particles by Fluids, by Martin Rhodes

-- 1: Fundamentals --

When a fluid is passed upwards through a bed of particles the pressure loss in the fluid due to frictional

resistance increases with increasing fluid flow. A point is reached when the upward drag force exerted by

the fluid on the particles is equal to the apparent weight of particles in the bed. At this point the particles

are lifted by the fluid, the separation of the particles increases, and the bed becomes fluidized. The force

balance across the fluidized bed dictates that the fluid pressure loss across the bed of particles is equal to

the apparent weight of the particles per unit area of the bed. Thus:

weight of particles - upthrust on particles

pressure drop = -------------------------------------------

bed cross sectional area

For a bed of particles of density p, fluidized by a fluid of density f to form a bed of depth H and voidage

in a vessel of cross sectional area A:

A plot of fluid pressure loss across the bed versus superficial fluid velocity through the bed would have

the appearance of Figure 1.

Figure 1: Pressure drop versus fluid velocity for packed and fluidized beds

The straight line region OA is the packed bed region. Here the solid particles do not move relative to one

another and their separation is constant. The pressure loss versus fluid velocity relationship in this region

is described in general by the Ergun equation, Equation 3. (See Rhodes, 1998, chapter 4 for a detailed

analysis of packed bed flow).

The region BC is the fluidized bed region where Equation 1 applies. At point A it will be noticed that the

pressure loss rises above the value predicted by Equation 1. This rise is more marked in powders which

have been compacted to some extent before the test and is associated with the extra force required to

overcome interparticle attractive forces.

The superficial gas velocity at which the packed bed becomes a fluidized bed is known as the minimum

fluidization velocity, Umf. This is also sometimes referred to as the velocity at incipient fluidization

("incipient" means "about to begin"). Umf increases with particle size and particle density and is affected

by fluid properties. It is possible to derive an expression for Umf by equating the expression for pressure

loss in a fluidized bed (Equation 2) with the expression for pressure loss across a packed bed. Thus

substituting the expression for (- p) for a fluidized bed from Equation 2 into the expression for (- p)

for a packed bed from Equation 3:

and so

where Ar is the dimensionless number known as the Archimedes number and Remf is the Reynolds

number at incipient fluidization,

In order to obtain a value of Umf from Equation 7 we need to know the voidage of the bed at incipient

fluidization, = mf. Taking mf as the voidage of the packed bed, we can obtain a crude Umf. However, in

practice voidage at the onset of fluidization may be considerably greater than the packed bed voidage. A

typical often used value of mf is 0.4. Using this value, Equation 7 becomes:

Wen and Yu (1966) produced an empirical correlation for Umf with a form similar to Equation 8: (Eq. 10 is

an alternate expression.)

The Wen and Yu correlation is valid for spheres in the range 0.01 < Remf < 1000.

For gas fluidization the Wen and Yu correlation is often taken as being most suitable for particles larger

than 100 m, whereas the correlation of Baeyens (1974) , shown below in Equation 11, is best for

particles less than 100 m.

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